Preheat the oven to 400 degrees F (200 degrees C). Spray a 9x13-inch baking pan or cast iron skillet with cooking spray; pour in about 1 teaspoon vegetable oil to coat the bottom.
Mix Parmesan, salt, garlic powder, paprika, and pepper together in a bowl.
Blot dry the cut-side of potatoes with a paper towel to remove any moisture.
Place potatoes in a bowl and drizzle with 1 tablespoon vegetable oil; toss until potatoes are lightly coated. Sprinkle potatoes with Parmesan mixture; toss to coat.
Arrange potatoes, cut-side down, on the prepared baking pan.
Bake in the preheated oven for 15 to 20 minutes. Flip potatoes and continue baking until golden and crispy, 15 to 20 more minutes. Serve with sour cream.